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41 students in a university travel club using the venn diagram show how many traveled to germany france and spain how many

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41 students in a university travel club. Using the venn diagram show how many traveled to Germany,France and Spain. How many students have been only to France? 14 members visited Germany,18 have been to Spain,18 have visited France,7 have visited Germany and France 8 have only been to Spain 5 have only been to Germany 5 have only been to Spain and France 3 have been to all three countries,some members have not been to any of the three

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Answer to a math question 41 students in a university travel club. Using the venn diagram show how many traveled to Germany,France and Spain. How many students have been only to France? 14 members visited Germany,18 have been to Spain,18 have visited France,7 have visited Germany and France 8 have only been to Spain 5 have only been to Germany 5 have only been to Spain and France 3 have been to all three countries,some members have not been to any of the three

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111 Answers

1. Start with the principle of inclusion-exclusion:

|G \cup F \cup S| = |G| + |F| + |S| - |G \cap F| - |G \cap S| - |S \cap F| + |G \cap F \cap S|

2. Plug in the given values:

41 = 14 + 18 + 18 - 7 - |G \cap S| - 5 + 3

3. Combine like terms:

41 = 46 - |G \cap S| - 5 - 7 + 3

41 = 46 - |G \cap S| - 9

4. Simplify the equation:

|G \cap S| = 46 - 9 - 41

|G \cap S| = 46 - 50

|G \cap S| = 6

The answer remains:

x = |G \cap S| = 6

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